1. Field of the Invention
The present invention relates to a pair of screw rotors used in a screw rotor machine for compressing or expanding a compressible fluid and supplying the compressed or expanded fluid and, more particularly, to a tooth profile curve thereof.
2. Discussion of the Background
Rotors having nonsymmetrical tooth profiles and used in a compressor or the like of a compressible fluid generally comprise a male rotor having helical lands with a major portion of each tooth profile outside the pitch circle thereof, and a female rotor having helical grooves with a major portion of each tooth profile inside the pitch circle thereof. Normally, the male rotor has a plurality of teeth, and the female rotor meshing therewith has a number of teeth slightly exceeding the number of teeth of the male rotor. The diameter of the tip circle of the male rotor is set to be substantially the same as that of the pitch circle of the female rotor.
A screw compressor or expander is constructed as follows. A pair of screw rotors of this type are rotatably housed inside a working space comprising two cylindrical bores formed in a casing. The cylindrical bores have parallel axes and have diameters equal to the outer diameter of the respective rotors to be arranged therein. The distance between the axes of the cylinders is shorter than the sum of the radii thereof, and the axial length of each cylindrical bore is the same as that of the rotors. The two end portions of the cylindrical bores are closed with end plates fixed to the casing. Inlet and outlet ports for the fluid are formed at predetermined positions of the casing (FIG. 3(a) or 3(b)).
When the above assembly is used as a compressor, the female rotor is rotated counterclockwise while the male rotor is rotated clockwise. With respect to the concave tooth profile of the groove of the female rotor, a curve at the front side along the rotating direction is referred to as the leading side tooth profile, and that at the rear side along the rotating direction is referred to as the trailing side tooth profile. Similarly, with respect to the convex tooth profile of the land of the male rotor, that at the front side along the rotating direction is referred to as the leading side tooth profile, and that at the rear side along the rotating direction is referred to as the trailing side tooth profile.
When the above assembly is used as an expander, the names of the respective curves are reversed. However, in the description to follow, the respective tooth profile curves will be explained in accordance with the above definitions.
FIGS. 1(a) and 1(b) show the respective tooth profile curves when the rotors are cut along a plane perpendicular to their rotating axes, i.e., the meshing state between the screw rotors at the end face of each rotor along the longitudinal axes thereof. FIG. 1(a) shows the phases of the tooth profiles of the two rotors immediately after the trailing side tooth profile curves of the male and female rotors have begun to contact each other. When the male rotor is rotated through about 20.degree. thereafter, the phases as shown in FIG. 1(b) are obtained wherein the highest portion of the tooth profile of the male rotor opposes the deepest portion of the groove of the tooth profile of the female rotor.
The above tooth profiles are conventional ones which are used in, for example, screw compressor manufactured by Hokuetsu Industries Co., Ltd. (Japanese Utility Model Registration No. 1432776) and have the following characteristics.
Referring to FIGS. 1(a) and 1(b), reference numeral 1 denotes a male rotor; and 2 a female rotor meshed therewith. The rotors 1 and 2 rotate about centers of rotation 3 and 4 (centers of the pitch circles) inside cylindrical bores of a casing (not shown) in the direction indicated by arrows, respectively, so as to serve as a fluid compressor. Reference numerals 15 and 16 respectively denote pitch circles of male rotor 1 and female rotor 2. A line connecting the centers of rotation 3 and 4 passes a contact point 17 between the pitch circles 15 and 16, i.e., a pitch point 17.
The above-mentioned tooth profiles will be described with reference to FIG. 1(b).
(1) Female Rotor Tooth Profile
(i) Leading side curve: The leading side curve is formed such that it consists of a circular arc (11-12) which extends from a point 12 at the deepest tooth profile portion of the groove of the female rotor to an outermost end 10 of the tooth profile and has a radius r.sub.4 with respect to the pitch point 17 which is the center of the arc (11-12), the portion between points 11 and 10 and extending from the arc (11-12) is a straight line (10-11) passing through the rotating center 4 of the female rotor and being circumscribed the arc (11-12) having the radius r.sub.4, the curve between points 12 and 13 of the bottom land of the groove of the female rotor is a circular arc (12-13) which has a radius r.sub.2 with the rotating center 4 of the female rotor as the center of the arc, and a portion between points 10 and 14 on the outer diameter of the tip circle coincides with the pitch circle 16 of the female rotor.
(ii) Trailing side curve: The trailing side curve is formed such that the curve between points 13 and 14 at the trailing side of the groove of the female rotor is set as an epitrochoidal curve generated by a point 8 on the tooth profile of the male rotor.
(2) Male Rotor Tooth Profile
(i) Leading side curve: The leading side curve is formed such that a curve (7-6) from a tip 7 of the male rotor tooth profile to a point 6 toward a point 5 at an innermost portion of the male rotor tooth profile is a circular arc with the contact point (pitch point) 17 between the pitch circles 15 and 16 of the two rotors serving as the center of the arc and has a radius r.sub.3 which is smaller than the radius r.sub.4 by an amount required for rotation, and a curve (6-5) from the point 6 to the innermost portion 5 is an envelope which is developed by a line between points 10 and 11 of the female rotor.
(ii) Trailing side curve: The trailing side curve is formed such that a curve between points 7 and 8 at the trailing side of the male rotor tooth profile is a circular arc which has a radius r.sub.1 with the rotating center 3 of the pitch circle 15 of the male rotor as the center of the arc, a curve (8-9) between a point 8 and a point 9 at an innermost portion of the male rotor tooth profile is an epicycloidal curve generated by a point 14 at the outermost portion of the groove of the female rotor, a curve between points 9 and 5 of the bottom of the groove coincides with the pitch circle 15 of the male rotor, and the point 8 reaches the intersection, on the sealing line along the thread ridge, which is at the sealed side of the cylindrical bores of the working space of the compressor. The point 8 is determined to be distant from a line (X-axis) connecting the centers of rotation 3 and 4 of the two rotors.
Since the conventional tooth profiles shown in FIG. 1(b) are defined as described above have following advantages,
(i) The blo hole between the working spaces can be set at substantially 0.
(ii) In the tooth profiles shown in FIG. 1(b), since the point 8 of the male rotor tooth profile is determined to be distant from the X-axis, the ratio of volume expansion of a space 18 defined at the contact portion between the tooth profiles of the male and female rotors upon rotation of the rotors is smaller than that obtained with the SRM tooth profiles (to be described later). Therefore, the power loss due to a vacuum produced in the space 18 upon volume expansion is small.
Despite these advantages, the conventional tooth profiles have the following disadvantages:
(iii) The volume of the working space is small (the stroke volume is small).
(iv) Since the bottom of the groove of the female rotor tooth profile has projections and recesses, a complete seal cannot be provided. The size measurement is difficult to obtain during machining. The cutter profile for machining the rotor also has projections and recesses and is complex and is inefficient in machining.
(v) Since the trailing side tooth profile curve is point-generated, the seal point wears easily and the sealing effect cannot be maintained over a long period of time.
(iv). Since the pressure angle of the tooth profile near the pitch circle is substantially 0, precise machining is difficult and the life of the machining tool is also short. The life of a hob tool is particularly short when screw rotors are hobbed.
A contact surface 18' in the initial meshing phases of the tooth profiles shown in FIG. 1(a) forms a space 18 in the phases shown in FIG. 1(b) in which the rotor 1 has rotated through about 20.degree. from the state shown in FIG. 1(a). Thus, the space 18 is exposed to vacuum by expanding and causes a power loss regardless of compression operation. For this reason, it is preferable to reduce the volume of trapped space 18. The tooth profile with the characteristics described above has a smaller ratio of volume expansion of the space 18 as compared to one to be described below.
For example, in one type of conventional tooth profile called the SRM tooth profile, the rotor used in a screw rotor machine as described in U.S. Pat. No. 3,423,017 has the tooth profile as shown in FIG. 2. The same reference appear in FIGS. 1(a) and 1(b) denote the same parts in FIG. 2, and a detailed description thereof will thus be omitted. The meshing phases in FIG. 2 correspond to those in FIGS. 1(a) and 1(b). Referring to FIG. 2,
(1) Female Rotor Tooth Profile
(i) Leading side curve: line (28-29); a circular arc having a point 36 on a straight line (17-29) as the center of the arc and a radius r'.sub.1, and a circular arc (29-30) having a pitch point 17 as the center of the arc and a radius r'.sub.2.
(ii) Trailing side curve: curve (30-31); an epitrochoidal curve generated by a point 23 on the male rotor tooth profile, line (31-32); a part of a curve passing through the center of rotation 4 of the male rotor, curve (32-33); a circular arc having the center of the arc on the pitch circle 16, curve (33-34); a circular arc having the center of rotation 4 as the center of the arc, and line (34-35); a circular arc having the center of the arc on the pitch circle 16.
(2) Male Rotor Tooth Profile
(i) Leading side curve: curve (21-22); an envelope developed by the arc (28-29) of the female rotor tooth profile, curve (22-23); a circular arc having the pitch point 17 as the center of the arc and a radius r'.sub.2.
(ii) Trailing side curve: curve (23-24); an epitrochoidal curve generated by a point 31 on the female rotor tooth profile, curve (24-25); a curve generated by a curve (31-32), curve (25-26); a circular arc having the center of the arc on the pitch circle 15, curve (26-27); a circular arc having the center of rotation 3 as the center of the arc, and line (27-21); an arc having the center on the pitch circle 15.
The volume of the space 18 in the SRM tooth profile which is to be exposed to vacuum is significantly larger than that in the tooth profile shown in FIG. 1(b).
When both the male and female rotors are at the rotating positions shown in FIG. 2(a), they contact at three points 31, 30 and 69 so that the compressed fluid will not leak. Due to the presence of these three contact points, a space 73 is formed at the leading side (upper side from the X-axis in FIG. 2(a)) of the male rotor, while a similar space 18 is formed at the trailing side (lower side from the X-axis in FIG. 2(a)) of the male rotor. Assume that the space 18 is sealed by an end face 67 (FIG. 3(a)) at the inlet side ends of the rotors, and the male and female rotors continue to rotate in the direction indicated by the arrow in FIG. 2(a). Then, the volume of the space 18 is gradually increased, and the degree of vacuum inside the space 18 (to be referred to as a vacuum space) is increased. As compared to the tooth profile shown in FIG. 1(b), the size of the vacuum space is significantly larger. As for an end face 68 (FIG. 3(a)) at the outlet side ends of the rotors, immediately before the space 73 opens into the end face 68, such gradually decreases in volume as the two rotors rotate and finally becomes substantially zero. Therefore, the gas trapped in the space 73 is compressed to an abnormal pressure. In a hydraulically-cooled rotary compressor, the lubricating fluid is injected into the working space for lubricating and cooling the contact and bearing portions. Therefore, the lubricating fluid being trapped inside the space 73 receives compression. As a result, as the rotors rotate, abnormal vibration or noise is generated and, in a worst case, the rotors wear or are damaged. In addition, a large drive torque is required for driving the compressor. Then, since an immoderate load is exerted on the rotors and the casing, a power loss is large and the life of bearings of the rotor shafts is shortened.
In order to solve this problem, Japanese Patent Application Laid Open Gazette Nos. 58-214693 and 58-131388 propose means for preventing overcompression of a residual gas by forming a bypass hole 71 in a casing inner wall surface 70 at the outlet port side as shown in FIG. 2(b), so that the residual gas and lubricating fluid are evacuated into another low-pressure working space through this bypass hole 71, or by forming a recess with a large volume at the position of the bypass hole 71. However, these means render the structure of the compressor complex and expensive, and lowers the performance.